Satellite Positioning Systems (SPS) rely on the passive measurement of ranging signals broadcast by a number of satellites, or ground-based or airborne equivalents, in a specific constellation or group of constellations. An on-board clock is used to generate a regular and usually continual series of events, often known as ‘epochs’, whose time of occurrence is coded into a random or pseudo-random code (known as a spreading code). As a consequence of the pseudo-random or random features of the time epoch encoding sequence, the spectrum of the output signal is spread over a frequency range determined by a number of factors including the rate of change of the spreading code elements and the waveform used for the spreading signal. Typically, the spreading waveform is rectangular and has a sinc function power spectrum.
The ranging signals are modulated onto a carrier signal for transmission to passive receivers. Applications are known that cover land, airborne, marine and space use. Typically, binary phase shift keying is employed to modulate the carrier signal, which, itself, has a constant magnitude. Usually, at least two such signals are modulated onto the same carrier in phase quadrature. The resulting carrier signal retains its constant envelope but has four phase states depending upon the two independent input signals. However, it will be appreciated that two modulating signals do not need to have the same carrier magnitude. It is possible for a constant carrier magnitude of the combined signal to be maintained by appropriate selection of corresponding phases other than π/2 radians.
An example of such a satellite positioning system is the Global Positioning System (GPS). Generally, the GPS operates using a number of frequencies such as, for example, L1, L2 and L5, which are centred at 1575.42 MHz, 1227.6 MHz and 1176.45 MHz respectively. Each of these signals is modulated by respective spreading signals. As will be appreciated by those skilled in the art, a Coarse Acquisition (CA) code signal emitted by the GPS Satellite Navigation System is broadcast on the L1 frequency of 1575.42 MHz with a spreading code rate (chip rate) of 1.023 MHz. The CA has a rectangular spreading waveform and is categorised as BPSK-R1. The GPS signal structure is such that the signal broadcast by the satellites on the L1 frequency has a second component in phase quadrature, which is known as the precision code (P(Y) code) and made available to authorised users only. The P(Y) signal is BPSK modulated with a spreading code at 10.23 MHz with a magnitude which is 3 dB lower in signal power than the CA code transmission. Consequently, the Q component has a magnitude which is 0.7071 (−3 dB) of the magnitude of the I component. It will be appreciated by those skilled in the art that the phase angles of these states of these signals are ±35.265° in relation to the ±I axis (phase of the CA code signal as specified in ICD GPS 200C). One skilled in the art also appreciates that the P code is a function of or is encrypted by the Y code. The Y code is used to encrypt the P code. One skilled in the art appreciates that the L1 signal, containing both I & Q components, and the L2 signal can be represented, for a given satellite, i, asSL1i(t)=APPi(t)di(t)cos(ω1t)+ACci(t)di(t)sin(ω1t), andSL2i(t)=BPPi(t)di(t)cos(ω2t)where    AP and AC are the amplitudes of the P and CA codes, typically AP=2AC;    Bp is the amplitude of the L2 signal;    ω1 and ω2 are the L1 and L2 carrier frequencies;    pi(t) represents the P(Y) ranging code and is a pseudo-random sequence with a chip rate of 10.23 Mcbps. The P code has a period of exactly 1 week, taking values of +1 and −1;    ci(t) represents the CA ranging code and is a 1023 chip Gold code, taking values of +1 and −1;    di(t) represents the data message, taking values of +1 and −1.
A satellite constellation typically comprises 24 or more satellites often in similar or similarly shaped orbits but in a number of orbital planes. The transmissions from each satellite are on the same nominal carrier frequency in the case of code division access satellites (such as GPS) or on nearby related frequencies such as GLONASS. The satellites transmit different signals to enable each one to be separately selected even though several satellites are simultaneously visible.
The signals from each satellite, in a CDMA system like GPS, are distinguished from each one another by means of the different spreading codes and/or differences in the spreading code rates, that is, the pi(t) and ci(t) sequences. Nevertheless, as will be appreciated from the power spectrum 100 shown in FIG. 1 there remains significant scope for interference between the signals transmitted by the satellites. FIG. 1 shows power spectra 100 for the CA and P(Y) codes. The power spectrum 102 for the CA code has maximum power at the carrier frequency L1 and zeros at multiples of the fundamental frequency, 1.023 MHz, of the CA code. For example, it can be appreciated that zeros occur either side of the carrier frequency at ±1.023 MHz, ±2.046 MHz etc. Similarly, the power spectrum 104 for the P(Y) code has a maximum amplitude centred on the L1 and L2 frequencies, with zeros occurring at multiples of ±10.23 MHz as is expected with a sine function waveform.
It is known to further modulate the ranging codes using a sub-carrier, that is, a further signal is convolved with the P codes and/or CA codes to create Binary Offset Carrier (BOC) modulation as is known within the art see, for example, J. W. Betz, “Binary Offset Carrier Modulation for Radionavigation”, Navigation, Vol. 48, pp 227-246, Winter 2001-2002. Standard BOC modulation 200 is illustrated in FIG. 2. FIG. 2 illustrates the combination of a portion of a CA code 202 with a subcarrier signal to produce the BOC signal 204 used to modulate a carrier such as, for example, L1. It can be appreciated that the BOC signal is a rectangular square wave and can be represented as, for example, ci(t)*sign(sin(2πfst)), where fs is the frequency of the subcarrier. One skilled in the art understands that BOC(fs, fc) denotes Binary Offset Carrier modulation with a subcarrier frequency of fs and a code rate (or chipping rate) of fc. Using binary offset carriers results in the following signal descriptions of the signals emitted from the satellite:SL1i(t)=Amscim(t)mi(t)di(t)cos(ω1t)+Acscig(t)gi(t)di(t)sin(ω1t)=ISL1i(t)+QSL1i(t), andSL2i(t)=Bmscim(t)mi(t)di(t)cos(ω2t)where                Am, Ac and Bm are amplitudes;        mi(t) is an m-code BOC(10,5) signal;        gi(t) is a Galileo open service range code;        scim(t) represents the sub-carrier signal for mi(t);        scig(t) represents a subcarrier signal for gi(t); and        ω1 and ω2 are the L1 and L2 carrier frequencies;        
FIG. 2 also illustrates power spectra for a BPSK-R1 code and pair of BOC signals, that is, BOC(2,1) and BOC(10,5). The first spectrum 202 corresponds to BPSK-R1 code. The second power spectrum 204 corresponds to the BOC(2,1) code and the third power spectrum 206 corresponds to the BOC(10,5) code. It can be appreciated that the side lobes 208 of the BOC(2,1) signal have a relatively large magnitude. Similarly, the illustrated side lobe 210 of the BOC(10,5) signal has a relatively large magnitude. One skilled in the art appreciates that the energy in the side lobes are a source of interference.
It is an object of embodiments of the present invention to at least mitigate the problems of the prior art.